Matter symmetries in supersymmetric standard models from non-invertible selection rules

TL;DR

This paper explores how non-invertible selection rules in supersymmetric models generate symmetries like R-parity, which prevent proton decay and baryon/lepton violation, offering a novel perspective beyond traditional discrete symmetries.

Contribution

It demonstrates that non-invertible fusion algebra symmetries can serve as R-parity and related protections in supersymmetric models, differing from conventional discrete symmetries.

Findings

A remnant $Z_2$ symmetry acts as R-parity at all-loop order.

Non-invertible selection rules lead to baryon triality and proton hexality.

These selection rules differ from traditional $Z_N$ symmetries in their effects.

Abstract

We discuss phenomenological implications of non-invertible selection rules in the framework of the supersymmetric standard model. We find that a remnant $\mathbb{Z}_2$ symmetry of fusion algebras which holds at all-loop order plays the role of $R$-parity, forbidding baryon and lepton violating operators. In addition, a combination of Standard Model gauge symmetry and the non-invertible selection rules lead to baryon triality and proton hexality that can protect the proton from decay. In general, our finding selection rules can not realize the same results as conventional $\mathbb{Z}_N$ symmetries in the supersymmetric standard model. We also clarify the assignments of matter fields under the fusion algebras that are consistent with $SU(4) \times SU(2) \times SU(2)$, $SU(5)$, and $SO(10)$ grand unified theories.